Nothing
###############################################################################
## get optimally robust IC for convex asymptotic risks
###############################################################################
setMethod("getInfRobRegTypeIC", signature(ErrorL2deriv = "UnivariateDistribution",
Regressor = "UnivariateDistribution",
risk = "asUnOvShoot",
neighbor = "UncondNeighborhood"),
function(ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
RegSymm, Finfo, trafo, upper, maxiter, tol, warn){
radius <- neighbor@radius
if(identical(all.equal(radius, 0), TRUE)){
if(warn) cat("'radius == 0' => (classical) optimal IC\n",
"in sense of Cramer-Rao bound is returned\n")
res <- getInfRobRegTypeIC(ErrorL2deriv = ErrorL2deriv, Regressor = Regressor,
risk = asCov(), neighbor = TotalVarNeighborhood(),
ErrorL2derivDistrSymm = ErrorL2derivDistrSymm,
RegSymm = RegSymm, Finfo = Finfo, trafo = trafo)
Risk <- getAsRiskRegTS(risk = risk, ErrorL2deriv = ErrorL2deriv,
Regressor = Regressor, neighbor = neighbor,
clip = res$b, cent = res$a, stand = res$A)
res$risk <- c(Risk, res$risk)
return(res)
}
bound <- risk@width*(-m1df(ErrorL2deriv, 0))*E(Regressor, abs)
if(is(neighbor, "ContNeighborhood")){
if(identical(all.equal(radius, 2*bound), TRUE)){
zi <- sign(as.vector(trafo))
A <- as.matrix(zi)
b <- zi*as.vector(trafo)*2*risk@width/radius
if(is(ErrorL2deriv, "AbscontDistribution"))
ws0 <- 0
else
ws0 <- d(ErrorL2deriv)(0)
if(is(Regressor, "AbscontDistribution"))
ws0x <- 0
else
ws0x <- d(Regressor)(0)
p0 <- ((1-p(Regressor)(0))*(p(ErrorL2deriv)(0)-ws0)
+ (p(Regressor)(0)-ws0x)*(1-p(ErrorL2deriv)(0)))
p1 <- ((1-p(Regressor)(0))*(1-p(ErrorL2deriv)(0))
+ (p(Regressor)(0)-ws0x)*(p(ErrorL2deriv)(0)-ws0))
ws00 <- 1 - p0 - p1
if(zi == 1)
a <- -b*p1/(1-ws00)
else
a <- b*p0/(1-ws00)
info <- paste("optimally robust IC for", sQuote(class(risk)[1]))
Risk <- list(asUnOvShoot = 0.5)
return(list(A = A, a = a, b = b, d = 1, risk = Risk, info = info))
}
if(radius > 2*bound)
stop("boundedness condition is violated!")
}
if(is(neighbor, "TotalVarNeighborhood")){
if(identical(all.equal(radius, bound), TRUE)){
zi <- sign(as.vector(trafo))
A <- as.matrix(zi)
b <- zi*as.vector(trafo)*risk@width/radius
if(is(ErrorL2deriv, "AbscontDistribution"))
ws0 <- 0
else
ws0 <- d(ErrorL2deriv)(0)
if(is(Regressor, "AbscontDistribution"))
ws0x <- 0
else
ws0x <- d(Regressor)(0)
p0 <- ((1-p(Regressor)(0))*(p(ErrorL2deriv)(0)-ws0)
+ (p(Regressor)(0)-ws0x)*(1-p(ErrorL2deriv)(0)))
p1 <- ((1-p(Regressor)(0))*(1-p(ErrorL2deriv)(0))
+ (p(Regressor)(0)-ws0x)*(p(ErrorL2deriv)(0)-ws0))
ws00 <- 1 - p0 - p1
if(zi == 1)
a <- -b*p1/(1-ws00)
else
a <- b*p0/(1-ws00)
info <- paste("optimally robust IC for", sQuote(class(risk)[1]))
Risk <- list(asUnOvShoot = 0.5)
return(list(A = A, a = a, b = b, d = 1, risk = Risk, info = info))
}
if(radius > bound)
stop("boundedness condition is violated!")
}
z <- 0
b <- 0
if(is(ErrorL2derivDistrSymm, "SphericalSymmetry"))
z.comp <- !(ErrorL2derivDistrSymm@SymmCenter == 0)
else
z.comp <- TRUE
iter <- 0
repeat{
iter <- iter + 1
b.old <- b
z.old <- z
b <- try(uniroot(getInfClipRegTS, lower = .Machine$double.eps^0.75,
upper = upper, tol = tol, ErrorL2deriv = ErrorL2deriv,
Regressor = Regressor, risk = risk, neighbor = neighbor,
z.comp = z.comp, cent = z)$root, silent = TRUE)
if(!is.numeric(b)){
if(warn) cat("Could not determine optimal clipping bound!\n",
"=> the minimum asymptotic bias (lower case) solution is returned\n")
res <- getInfRobRegTypeIC(ErrorL2deriv = ErrorL2deriv, Regressor = Regressor,
risk = asBias(), neighbor = neighbor,
ErrorL2derivDistrSymm = ErrorL2derivDistrSymm,
trafo = trafo, maxiter = maxiter, tol = tol, warn = warn)
Risk <- getAsRiskRegTS(risk = risk, ErrorL2deriv = ErrorL2deriv,
Regressor = Regressor, neighbor = neighbor,
clip = res$b, cent = res$a, stand = res$A,
trafo = trafo)
res$risk <- c(Risk, res$risk)
return(res)
}
z <- getInfCentRegTS(ErrorL2deriv = ErrorL2deriv, Regressor = Regressor,
neighbor = TotalVarNeighborhood(radius = neighbor@radius),
clip = b, cent = z, z.comp = z.comp)
prec <- max(abs(b-b.old), abs(z-z.old))
# cat("current precision in IC algo:\t", prec, "\n")
if(is(Regressor, "UnivariateDistribution") & (!z.comp)) break
if(prec < tol) break
if(iter > maxiter){
cat("maximum iterations reached!\n", "achieved precision:\t", prec, "\n")
break
}
}
A <- getInfStandRegTS(ErrorL2deriv = ErrorL2deriv, Regressor = Regressor,
neighbor = TotalVarNeighborhood(), clip = b, cent = z)
info <- paste("optimally robust IC for", sQuote(class(risk)[1]))
Risk <- getAsRiskRegTS(risk = risk, ErrorL2deriv = ErrorL2deriv,
Regressor = Regressor, neighbor = neighbor,
clip = b, cent = z, stand = A)
return(list(A = as.matrix(A), a = A*z, b = A*b, d = NULL, risk = Risk, info = info))
})
setMethod("getInfRobRegTypeIC", signature(ErrorL2deriv = "UnivariateDistribution",
Regressor = "UnivariateDistribution",
risk = "asUnOvShoot",
neighbor = "CondNeighborhood"),
function(ErrorL2deriv, Regressor, risk, neighbor, ErrorL2derivDistrSymm,
RegSymm, Finfo, trafo, upper, maxiter, tol, warn){
radiusCurve <- neighbor@radiusCurve
if(is(Regressor, "AbscontDistribution")){
xlower <- ifelse(is.finite(q.l(Regressor)(0)), q.l(Regressor)(0), q.l(Regressor)(getdistrOption("TruncQuantile")))
xupper <- ifelse(is.finite(q.l(Regressor)(1)), q.l(Regressor)(1), q.l(Regressor)(1 - getdistrOption("TruncQuantile")))
x.vec <- seq(from = xlower, to = xupper, length = 1000)
}else{
if(is(Regressor, "DiscreteDistribution"))
x.vec <- support(Regressor)
else
x.vec <- unique(r(Regressor)(getdistrOption("RtoDPQ.e")))
}
radCx <- radiusCurve(x.vec)
if(identical(all.equal(max(radCx), 0), TRUE)){
if(warn) cat("'radiusCurve == 0' => (classical) optimal IC\n",
"in sense of Cramer-Rao bound is returned\n")
res <- getInfRobRegTypeIC(ErrorL2deriv = ErrorL2deriv, Regressor = Regressor,
risk = asCov(), neighbor = CondTotalVarNeighborhood(),
ErrorL2derivDistrSymm = ErrorL2derivDistrSymm,
RegSymm = RegSymm, Finfo = Finfo, trafo = trafo)
Risk <- getAsRiskRegTS(risk = risk, ErrorL2deriv = ErrorL2deriv,
Regressor = Regressor, neighbor = neighbor,
clip = res$b, cent = res$a, stand = res$A)
res$risk <- c(Risk, res$risk)
return(res)
}
bound <- 1/(risk@width*(-m1df(ErrorL2deriv, 0)))
if(is(neighbor, "CondContNeighborhood")){
test <- abs(x.vec) - radCx*bound/2
if(identical(all.equal(max(test), 0), TRUE) & any(test == 0)){
if(!is(RegDistr, "AbscontDistribution"))
if(!identical(all.equal(d(Regressor)(0), 0), TRUE))
stop("Solution only available under 'K(x=0)!=0'!")
stop("boundary case not yet implemented")
}
if(all(test < 0))
stop("boundedness condition is violated!")
}
if(is(neighbor, "CondTotalVarNeighborhood")){
test <- abs(x.vec) - radCx*bound
if(identical(all.equal(max(test), 0), TRUE) & any(test == 0)){
if(!is(RegDistr, "AbscontDistribution"))
if(!identical(all.equal(d(Regressor)(0), 0), TRUE))
stop("Solution only available under 'K(x=0)!=0'!")
stop("boundary case not yet implemented")
}
if(all(test < 0))
stop("boundedness condition is violated!")
}
z.vec <- numeric(length(x.vec))
b.vec <- numeric(length(x.vec))
if(is(ErrorL2derivDistrSymm, "SphericalSymmetry"))
z.comp <- !(ErrorL2derivDistrSymm@SymmCenter == 0)
else
z.comp <- TRUE
iter <- 0
repeat{
iter <- iter + 1
b.old <- b.vec
z.old <- z.vec
for(i in 1:length(x.vec)){
if(test[i] <= 0){ # covers x == 0
b.vec[i] <- 0
z.vec[i] <- 0
}else{ # here: x != 0
b.vec[i] <- try(uniroot(getInfClipRegTS, lower = .Machine$double.eps^0.75,
upper = upper, tol = tol, ErrorL2deriv = ErrorL2deriv,
Regressor = x.vec[i], risk = risk, neighbor = neighbor)$root,
silent = TRUE)
z.vec[i] <- getInfCentRegTS(ErrorL2deriv = ErrorL2deriv, Regressor = x.vec[i],
neighbor = CondTotalVarNeighborhood(radius = neighbor@radius,
radiusCurve = neighbor@radiusCurve),
clip = b.vec[i], cent = z.vec[i], z.comp = z.comp)
}
}
prec <- max(abs(b.vec-b.old), abs(z.vec-z.old))
# cat("current precision in IC algo:\t", prec, "\n")
if(is(Regressor, "UnivariateDistribution") & (!z.comp)) break
if(prec < tol) break
if(iter > maxiter){
cat("maximum iterations reached!\n", "achieved precision:\t", prec, "\n")
break
}
}
if(is(Regressor, "DiscreteDistribution")){
bfun <- function(x){
ind <- (round(x, 8) == round(x.vec, 8))
if(any(ind))
return(b.vec[ind])
else
return(NA)
}
zfun <- function(x){
ind <- (round(x, 8) == round(x.vec, 8))
if(any(ind))
return(z.vec[ind])
else
return(NA)
}
}else{
if(is.finite(q.l(Regressor)(0))){
yleft.b <- NA
yleft.z <- NA
}else{
yleft.b <- b.vec[1]
yleft.z <- z.vec[1]
}
if(is.finite(q.l(Regressor)(1))){
yright.b <- NA
yright.z <- NA
}else{
yright.b <- b.vec[length(b.vec)]
yright.z <- z.vec[length(z.vec)]
}
zfun <- approxfun(x.vec, z.vec, yleft = yleft.b, yright = yright.b)
bfun <- approxfun(x.vec, b.vec, yleft = yleft.z, yright = yright.z)
}
A <- getInfStandRegTS(ErrorL2deriv = ErrorL2deriv, Regressor = Regressor,
neighbor = CondTotalVarNeighborhood(), clip = bfun, cent = zfun)
info <- paste("optimally robust IC for", sQuote(class(risk)[1]))
Risk <- getAsRiskRegTS(risk = risk, ErrorL2deriv = ErrorL2deriv,
Regressor = Regressor, neighbor = neighbor,
clip = bfun, cent = zfun, stand = A)
bfct <- function(x){bf <- bfun; A * bf(x)}
body(bfct) <- substitute({bf <- bfun; A * bf(x)}, list(bfun = bfun, A = A))
b <- RealRandVariable(Map = list(bfct), Domain = Reals())
afct <- function(x){z <- zfun; A * z(x)}
body(afct) <- substitute({z <- zfun; A * z(x)}, list(zfun = zfun, A = A))
a <- RealRandVariable(Map = list(afct), Domain = Reals())
return(list(A = as.matrix(A), a = a, b = b, d = NULL, risk = Risk, info = info))
})
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